Algebra worksheet — GCSE Foundation

1.The graph of y = x² − 7x + 2 crosses the x-axis at two points. One root, read from the graph, is approximately x = 0.30. Using the fact that the sum of the two roots of x² − 7x + 2 = 0 is 7, estimate the other root, correct to 2 decimal places.

2.y = x + 10. Work out the value of y when x = 0.

3.A stack of firewood has 3 logs in the top layer. Each layer below has 4 more logs than the layer above it. Work out the number of logs in the 6th layer from the top.

4.Expand 2(x − 13)

5.A straight line passes through the points (1, 3) and (2, 5). Work out the equation of the line.

6.Make x the subject of the formula y = 3(x + 2).

7.The solution set of x ≥ −1 is drawn on a number line. Which description of that number line is correct?

8.A sequence has the position-to-term rule n² − 3, where n is the position number. Work out the difference between the 6th term and the 5th term.

9.The graph of y = (x − 2)(x + 5) crosses the x-axis at two points. Work out the x-coordinates of these two points.

10.Make x the subject of the formula y = 5x + 3.

11.The first four terms of a sequence are 9, 14, 19, 24. Work out an expression, in terms of n, for the nth term.

12.Tom buys 2 notebooks and 6 pencils on Monday, priced at p pence each for a notebook and q pence each for a pencil. On Tuesday he buys 3 more notebooks and 1 more pencil. Write a simplified expression, in pence, for the total amount Tom has spent on notebooks and pencils.

13.A car's speed increases steadily while it accelerates. Its speed v m/s after t seconds is given by v = u + at, where u is the starting speed in m/s and a is the acceleration in m/s². A car starts at u = 4 m/s and accelerates at a = 2 m/s² until it reaches v = 20 m/s. Work out t, the time taken in seconds.

14.Solve 5(x + 3) = 40

15.Work out the value of 5m² + 3m when m = −2.4